8
Lecture 8: February 21, 2006
8.1
More Nonlinear Systems
The lower bound for the VC matrix for the 2SLS estimator in a non-linear system is
as follows:
V C = 11 plim T [(EZ1 ) (EZ1 )]1 .
Proof: If we use the instruments X K , the VC matrix can be writte
Proof:
n
fn (y, x)dy =
n1 h(k+1)
n
y Yj x Xj
,
dy
hn
hn
K
j =1
same subsitution: zj = (y Yj )/hn , dy = hn dzj
n
=
n1 h(k+1)
n
K zj ,
j =1
n
= n1 hk
n
K zj ,
j =1
n
= n1 hk
n
K
j =1
x Xj
hn dzj
hn
x Xj
dzj
hn
x Xj
hn
= fn (x)
QED.
Next, lets see what the
Somehow (?):
P ost(B, |data)
1
T +1
exp
1
(Y XB ) (Y XB ) .
2 2
And applying the same technique as in the last application,
P ost(B, |data)
1
T +1
exp
1
( + (B B ) X X (B B ) .
2 2
This is expressible as the product of a marginal, g1 ( ) and a cond
Economics 722: Econometrics
Harry Kelejian
Matthew Chesnes
Updated: May 11, 2006
1
Lecture 1: January 26, 2006
1.1
Topics in Linear Systems: Truncated 2SLS and 3SLS
Sometimes our X matrix, T xK , is such that T < K , so X X is singular and 2SLS
cannot be